ABSTRACT
This chapter begins with two classroom examples, including some of the thinking behind their planning and offers them to provoke thinking about what can be planned and what must remain unexpected, if a teacher aims to “create the conditions in which creative and independent work can take place”. The distinction the teacher needs students to make, in setting up this task, is that shapes are labelled by adding up the number of dots inside and on the outside. The teacher cannot know what the students will notice, but is confident that there will be some things noticed that allow tasks to be set up for the class, related to the problem. It does not really matter what particular things are said, so long as they can lead to questions, challenges or conjectures. There seems to be something powerful in using students' names to label conjectures.
